장혜원 Chang Hyewon

DOI:10.7468/jksmee.2025.39.2.107 JANT Vol.39(No.2) 107-122, 2025

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Mathematical terms, while fostering conceptual understanding, can also become a source of learning difficulty, requiring careful instructional attention. In school mathematics, terms such as the "length and width(Strictly speaking, unlike the Korean terms '세로' and '가로', length and width are not inherently relative, but are simply the corresponding English expressions)" of a rectangle and the "upper and lower bases" of a trapezoid reflect relativity, as their naming often depends on the figure’s orientation or position. This relativity can introduce ambiguity when referring to components of figures, which may in turn lead to conceptual confusion and hinder subsequent mathematical learning. This study critically examines the use of such relative terms in geometry and proposes instructional considerations and directions for improvement. Through a longitudinal analysis of textbooks across multiple curriculum periods, the research identifies several issues: mismatches between mathematical terms and their everyday meanings, a lack of awareness of relativity, inconsistencies between two- and three-dimensional figures in terminology, conceptual meaning, and content domains, and tensions with mathematical diversity. Based on these findings, the study highlights the need to raise awareness of the relative nature of terms such as “length and width”, and calls for a re-evaluation of terms like "upper and lower bases" in educational settings.

박미미 Park Mimi , 이은정 Lee Eunjung

DOI:10.7468/jksmee.2025.39.2.123 JANT Vol.39(No.2) 123-146, 2025

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The equal sign serves as a foundational symbol for developing algebraic thinking in elementary mathematics. To support this development, it is essential that students progress from an operational view of the equal sign to a relational understanding. This study investigates how tasks aimed at fostering relational understanding of the equal sign are incorporated in elementary mathematics textbooks from the United States and Australia―two countries whose curricula explicitly address equality and equivalence. Using both frequency analysis and qualitative analysis by task type, the study reveals that while both countries offer a range of task types to support relational understanding, there are notable differences in when and how these tasks are introduced. The findings highlight key features of effective tasks and offer implications for improving how the concepts of equality and equivalence are addressed in Korea’s revised mathematics curriculum and textbook development.

이윤경 Lee Yoon Kyong , 오영열 Oh Young Youl

DOI:10.7468/jksmee.2025.39.2.147 JANT Vol.39(No.2) 147-170, 2025

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This study investigates the characteristics of discourse types observed in strategic, epistemological, and social conflict situations during mathematical problem solving among fifth-grade elementary students. The aim is to analyze the structure of discourse emerging in such conflicts and to provide a practical foundation for instructional design that supports students’ cognitive processes, meaning construction, and collaborative communication in mathematics classrooms. To this end, 22 students from an elementary school in Seoul were grouped into 11 pairs based on their mathematics achievement levels and engaged in problem-solving tasks. A total of 33 discourse episodes were collected through audio and video recordings. The data were qualitatively analyzed using a restructured analytical framework that integrated the ATC21S collaborative problem-solving rubric by Hesse et al. (2015)―including metacognitive (reflective thinking), cognitive (divergent and convergent thinking), and social (prosocial and antisocial interaction) domains―with belief-oriented discourse types proposed by Kim (2012). The findings revealed distinct patterns across conflict types. In strategic conflicts, differences in solution strategies led to frequent use of information-sharing and explanatory discourse. In epistemological conflicts, differences in confidence, interpretation criteria, and individual beliefs gave rise to explanatory and negotiation/compromise discourse, often involving personal reasoning, prior knowledge, and justification. In social conflicts, interactions related to role distribution, turn-taking, and recognition triggered emotional-expression and negotiation/compromise discourse, shifting the focus from problem-solving to restoring social dynamics and collaboration. These results highlight that discourse in conflict situations functions as a complex interactive process that facilitates cognitive shifts, meaning negotiation, and collaborative resolution. The study underscores the importance of discourse-centered instructional design in promoting deeper mathematical thinking and effective classroom interaction.

방정숙 Pang Jeongsuk , 이지은 Lee Ji-eun

DOI:10.7468/jksmee.2025.39.2.171 JANT Vol.39(No.2) 171-192, 2025

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This study investigates how a redesigned “Patterns and Correspondence” unit, explicitly targeting the three meanings of variable―changing quantity, unknown, and generalized number―can be enacted in the classroom and how it influences students’ understanding. Two Grade 5 classes (eight lessons each) participated. Pre- and post-assessments captured shifts in students’ conceptions of the three meanings. Results indicate that exploring these meanings within a single context helped students discern the distinct roles of variables and differentiate among them. In particular, students’ understanding of variables improved as they interpreted them to represent a broader numerical range and recognized that the value of an unknown could be determined under given conditions. Through activities exploring symbolic representations, students began to conceptualize generalized numbers as denoting arbitrary rather than specific values. These findings offer practical insights for enriching elementary school instruction on variables.

양성현 Yang Seong Hyun , 이세형 Lee Se Hyung

DOI:10.7468/jksmee.2025.39.2.193 JANT Vol.39(No.2) 193-215, 2025

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Building blocks, which can provide students with a variety of spatial reasoning activities across dimensions, were introduced in the 7th curriculum to enhance students’ spatial sense, and have been playing a central role in the ‘shapes and measurements’ area in elementary schools to this day. Recently, various engineering tools have been proposed for teaching and learning building blocks, and the curriculum also emphasizes the use of various models and engineering tools when exploring three-dimensional figures made of building blocks. In this study, we analyzed building blocks-related content covered in 11 elementary school 6-2 mathematics textbooks and developed building blocks teaching and learning tool using GeoGebra to complement the shortcomings of existing engineering tools. The developed tool was applied to experimental classes by three teachers, and it was confirmed that it can be applied to all teaching and learning activities related to building blocks except for the Soma Cube used in textbooks. Through this, the educational usefulness of the developed tool was verified, and implications for building blocks related teaching and learning were derived.

김민정 Kim Min Jeong , 최인용 Choi Inyong

DOI:10.7468/jksmee.2025.39.2.217 JANT Vol.39(No.2) 217-241, 2025

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The 2022 revised mathematics curriculum emphasizes the development of students' abilities to communicate effectively about mathematical thinking and strategies, as well as to reason logically based on conjectures and justifications. Accordingly, the purpose of this study is to explore practical approaches to teaching mathematical argumentation in the classroom by analyzing the types of rebuttals and corresponding responses that appear during sixth-grade students' mathematical argumentation activities. For this purpose, a lesson was designed based on Lakatos’s methodology, focusing on the concept of the volume of rectangular prisms. The study was conducted with eight sixth-grade students from an elementary school located in Gyeonggi Province. Students’ activities were audio- and video-recorded, transcribed, and qualitatively analyzed. The results revealed that among the five types of rebuttals proposed by Verheij, four excluding rebuttals against the warrant were observed during the lessons. In response to rebuttals, students employed three major strategies: (1) presenting additional data or supporting arguments, (2) limiting claims through specifying conditions, and (3) modifying or withdrawing original claims. Based on these findings, this study proposes the applicability and educational implications of rebuttal-centered argumentation activities in elementary mathematics classrooms.

전태환 Jeon Tae Hwan , 이헌규 Lee Heon Kyu , 전대열 Jeon Daeyeol

DOI:10.7468/jksmee.2025.39.2.243 JANT Vol.39(No.2) 243-262, 2025

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In the era of AI, the importance of assessing mathematical proof skills and creativity has grown significantly in mathematics education. This study explores how the creativity of gifted students can be assessed through mathematical proof tasks within this context. The study analyzed the processes of mathematical justification and proof performed by first-year middle school students participating in a gifted education program at K University, evaluating four elements of creativity: fluency, flexibility, originality, and elaboration. The results revealed that elaboration plays a crucial role in the interaction between mathematical proof skills and creativity, significantly affecting students' performance and rankings when included in the assessment. Notably, elaboration was shown to reflect students' ability not merely to generate ideas, but to organize and express them systematically and logically, highlighting its essential role in creativity assessment. Consequently, the need for developing appropriate assessment tasks capable of evaluating elaboration was identified, and it was suggested that the type of assessment tasks used could lead to different student outcomes. This study proposes a systematic approach to integrating elaboration into assessments of mathematical creativity and emphasizes the need for objective and structured evaluation methods, while discussing directions for further in-depth research in this area.

서보억 Suh Bo Euk

DOI:10.7468/jksmee.2025.39.2.263 JANT Vol.39(No.2) 263-286, 2025

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This study investigates the changes in perception and the characteristics of teaching and learning that emerge when middle school students participate in mathematics field trip activities at cultural heritage sites. Focusing on Cheomseongdae and Bulguksa, two of Gyeongju’s most significant cultural landmarks, the research designed and implemented a series of activities before, during, and after the field trips. Both quantitative and qualitative analyses were conducted to examine students´ perceptions, interests, and learning processes. The findings reveal that engaging in mathematics exploration within real-world cultural heritage contexts enables students to apply mathematical concepts and principles in practice, fostering increased interest and pride in mathematics as well as collaborative inquiry skills. Furthermore, the study confirms that mathematics education grounded in authentic, real-life experiences positively influences students´ cognitive, affective, and cultural-mathematical development. These results underscore the value of integrating field-based learning into the mathematics curriculum to enhance students´ holistic understanding and engagement.

장현석 Chang Hyun Suk

DOI:10.7468/jksmee.2025.39.2.287 JANT Vol.39(No.2) 287-305, 2025

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In this study, 74 third-year high school students were surveyed for their understanding of the limits of sequences, and gender differences in concept images of the limit of sequences were analyzed. The results of developing a test tool based on previous research and applying it are as follows. First, when a constant expression is included in the sequence, the understanding of high school students is relatively lower than that of other questions. For example, there is a sequence in which infinite terms excluding finite number are constants and a sequence in which terms vibrating at the same interval as the constant term are combined. Second, the concept image about the convergence of sequences generally appeared in a form in which the concept of a fixed number and the concept of motion are combined, that is, 'get closer to one number'. On the other hand, the perception of the divergence of sequences appeared in various forms, that is, 'increases or decreases quantitatively'. Finally, this study considered the need to provide with various opportunities to reveal students’ conceptual images and make logical judgments through communication in the teaching and learning process related to the limit of sequences.

김정현 Kim Jung Hyun , 고호경 Ko Ho Kyoung

DOI:10.7468/jksmee.2025.39.2.307 JANT Vol.39(No.2) 307-325, 2025

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In a situation where intelligence, hyper-connected society, and human-machine collaboration are prominent (Nagwisu et al., 2018), it is necessary to provide appropriate help and feedback to students' learning levels and situations rather than limiting the role of helping with math learning to math teachers. Math learning coaching systematically approaches math learning for students who avoid and dislike math, inducing learning motivation and helping them to learn self-directedly (Kim Jeong-hyeon, 2021), but it is difficult for math teachers to do it alone. Accordingly, we surveyed the strategies for each stage of the math learning coaching model to examine teachers' perceptions of areas where artificial intelligence can be used in math learning coaching. As a result, it was said that artificial intelligence, which possesses a large amount of quantitative data, can analyze students and provide customized learning tailored to each student's characteristics based on that information, inducing students' learning motivation, providing sufficient opportunities for continuous learning, increasing students' success experiences, and fostering self-directed learning abilities through immediate feedback on learning results. Through this study, we aim to provide information on areas where math teachers can utilize artificial intelligence in math learning coaching.